Duflo isomorphism

From Wikipedia, the free encyclopedia

In mathematics, the Duflo isomorphism is an isomorphism between the center of the universal enveloping algebra of a finite-dimensional Lie algebra and the invariants of its symmetric algebra. It was introduced by Duflo (1977).

The isomorphism also follows from the Kontsevich formality theorem.

Properties

For a nilpotent Lie algebra the Duflo isomorphism coincides with the symmetrization map from symmetric algebra to universal enveloping algebra. For a semisimple Lie algebra the Duflo isomorphism is compatible in a natural way with the Harish-Chandra isomorphism.

References

  • Duflo, Michel (1977), "Opérateurs différentiels bi-invariants sur un groupe de Lie", Annales Scientifiques de l'École Normale Supérieure. Quatrième Série, 10 (2): 265–288, ISSN 0012-9593, MR 0444841 
  • Calaque, Damien; Rossi, Carlo A. (2011), Lectures on Duflo isomorphisms in Lie algebra and complex geometry (PDF), EMS Series of Lectures in Mathematics, European Mathematical Society (EMS), Zürich, ISBN 978-3-03719-096-8, MR 2816610 
Retrieved from "https://en.wikipedia.org/w/index.php?title=Duflo_isomorphism&oldid=646635728"
This content was retrieved from Wikipedia : http://en.wikipedia.org/wiki/Duflo_isomorphism
This page is based on the copyrighted Wikipedia article "Duflo isomorphism"; it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License (CC-BY-SA). You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA